1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Crystallization kinetics of clinopyroxene and titanomagnetite growing from a trachybasaltic 1
melt: New insights from isothermal time-series experiments 2
3
Alessio Pontesilli1, Matteo Masotta2, Manuela Nazzari3,4, Silvio Mollo3,4, Pietro Armienti2, 4
Piergiorgio Scarlato4, Marco Brenna1 5
6
1Department of Geology, University of Otago, PO Box 56, Dunedin 9054, New Zealand
7
2Dipartimento di Scienze della Terra, Università degli Studi di Pisa, Via S. Maria 53, 56126 Pisa,
8
Italy 9
3Dipartimento di Scienze della Terra, Sapienza-Università di Roma, P.le Aldo Moro 5, 00185
10
Roma, Italy 11
4Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Rome, Italy
12 13 14 Corresponding author: 15 Alessio Pontesilli 16 Department of Geology, 17 University of Otago, 18 PO Box 56, 19 Dunedin 9054, 20 New Zealand 21 Email: alessio.pontesilli@postgrad.otago.ac.nz 22 23 24 25 26 27 28 29 30 31 32 33 34
Manuscript (abstract, main text, figure captions, references)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 Abstract 35
In order to investigate the role of crystallization kinetics in mafic alkaline systems, textural 36
measurements, mineral compositional changes and diffusion modelling calculations have been 37
carried out on isothermal time-series experiments. The data were obtained at 400 MPa and 1,100 °C 38
under anhydrous (nominally 0 wt.% H2O) and hydrous (2 wt.% H2O added) conditions. A synthetic
39
trachybasaltic melt was first heated up to the superliquidus temperature of 1,300 °C and then 40
rapidly cooled at 80 °C/min down to 1,100 °C. The final target temperature was kept constant over 41
variable dwell times in the range of 0.5-24 h. Estimates of area fractions, crystal sizes, crystal size 42
distributions and surface area to volume ratios indicate the attainment of fast crystal growth kinetics 43
at the shortest experimental run duration, with early achievement of stable crystal sizes for 44
clinopyroxene and titanomagnetite. The surface area to volume ratio weakly decreases with 45
increasing dwell time, according to the development of euhedral crystal morphologies. Crystal 46
growth rates are also observed to progressively decrease from 0.5 to 24 h. Due to the effect of fast 47
growth kinetics, the morphological maturation of clinopyroxene progresses by attachment of 48
dendrite branches, infilling and overgrowth phenomena, leading to the formation of well-faced and 49
euhedral crystals. The kinetically-controlled cation exchange (Si + Mg) (TAl + Fe3+) controls the 50
clinopyroxene compositional variation, expanding the stability of Tschermak component at the 51
expense of diopside. Conversely, titanomagnetite is characterized by an almost constant 52
composition that, however, is enriched in incompatible Al and Mg cations, as typically observed 53
under rapid crystal growth conditions. Titanomagnetite crystals show always euhedral morphology 54
that develops by heterogeneous nucleation on early-formed clinopyroxene dendrites. With 55
increasing dwell time, the textural maturation of clinopyroxene reduces the number of 56
heterogeneous nucleation sites and the titanomagnetite growth proceeds by coarsening. Overall, the 57
effect of undercooling causes strong supersaturation phenomena in the trachybasaltic melt, resulting 58
in enhanced nucleation kinetics and fast attainment of a high crystallinity. As the dwell time 59
increases, the bulk system tends to minimize the interfacial free energy between crystals and 60
surrounding melt. This results in the progressive replacement of the early dendritic shapes 61
developed in a diffusion-limited growth regime, by the formation of euhedral morphologies typical 62
of interface-limited regimes that still retain the chemical evidences of the dendritic stage as complex 63
zoning patterns in clinopyroxene. 64
65
Keywords: Crystallization kinetics; undercooling; clinopyroxene; titanomagnetite; textural 66
analysis; rapid crystal growth 67
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 1. Introduction 69
The textural features of igneous rocks represent a valuable source of information for better 70
understanding the physicochemical conditions of magmas at which crystals nucleate and grow (e.g. 71
Cashman 1990, 1993; Armienti et al., 1994, 2013; Cashman and Blundy, 2000; Hammer, 2006, 72
2008; Resmini, 2007; Armienti, 2008). In this context, crystallization kinetics exert an important 73
role in the solidification of the melt into a rock(e.g. Cashman and Marsh, 1988; Marsh, 1988, 1998; 74
Hersum and Marsh, 2006; Higgins, 1998, 2006; Zieg and Lofgren, 2006; Spillar and Dolejs, 2013; 75
Mollo and Hammer, 2017). A great number of experimental studies has been conducted on either 76
natural or synthetic silicate liquids of variable compositions, in order to provide constraints on the 77
textural and chemical changes of minerals under the effects of variable degrees of undercooling 78
caused by either cooling (e.g., Lofgren et al., 1974; Donaldson, 1976; Walker et al.,1976, 1978; 79
Kirkpatrick, 1981; Lofgren and Russell, 1986; Pupier et al., 2008; Del Gaudio et al., 2010; Mollo et 80
al., 2011, 2012a, 2013a, 2013b; Iezzi et al., 2013) or decompression (e.g., Hammer and Rutherford, 81
2002, Couch et al., 2003; Hammer, 2008; Brugger and Hammer, 2010a; Waters et al., 2015). 82
Undercooling, expressed as the difference between the liquidus and experimental temperatures (∆T 83
= Tliq-Texp), can be experimentally controlled by either varying the liquidus temperature (by
84
changing the melt H2O content) or the final target temperature (by applying variable cooling rates)
85
(cf. Hammer, 2008; Mollo & Hammer, 2017). Ostwald ripening, crystal coalescence, grain 86
boundary migration, and infilling of early crystal framework are primary controlled by the 87
undercooling and documented as the effective mechanisms controlling the textural features of the 88
experimental products (Hammer and Rutherford, 2002; Simakin et al., 2003, Zieg and Lofgren, 89
2006; Pupier et al., 2008; Schiavi et al., 2009; Mollo at al., 2010; Iezzi et al., 2011, 2014; Ni et al., 90
2014; Welsch et al., 2014; Shea et al., 2015). The significance of these textural maturation 91
mechanisms has been also assessed through specifically designed laboratory (Park and Hanson, 92
1999; Cabane et al., 2001, 2005) and natural (Higgins, 1998, 1999; O’Driscoll et al., 2007; Higgins 93
and Roberge, 2003; Mollo et al., 2015a) investigations, as well as through experimental analogs 94
(Means and Park, 1994) and numerical modelling (Hersum and Marsh, 2006). However, in spite of 95
this extensive literature, a few experimental studies have clearly addressed the role of relaxation 96
kinetics on crystal growth when the resting temperature is kept constant over different dwell times, 97
after an early stage of undercooling (cf. Mollo et al., 2012a). 98
In this study, we present new textural and chemical data on clinopyroxene and 99
titanomagnetite crystals obtained through isothermal time-series experiments conducted on a 100
synthetic trachybasalt rapidly undercooled before crystallization. The imposed degree of 101
undercooling is the thermodynamic driving force inducing early nucleation of clinopyroxene and 102
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
titanomagnetite, whilst the crystal growth and textural maturation proceeded isothermally over time. 103
The effects of crystallization kinetics and possible equilibration phenomena with increasing dwell 104
time are quantified in terms of mineral and glass compositions, total crystallinity, maximum crystal 105
size, and crystal size distribution analysis. Textural data are also compared with the diffusion length 106
of chemical elements in the melt (i.e., modeling data from Zhang et al., 2010), in order to 107
discriminate the influence of diffusion- and interface-limited growth on the disequilibrium or near-108
equilibrium compositions of minerals (Lofgren et al., 2006; Hammer, 2008; Watson & Muller, 109
2009; Mollo and Hammer, 2017), and the potential relationship with observed crystal morphologies 110
(Sunagawa, 1981, 2005; Faure et al., 2007). This comparative approach provides new insights on 111
the solidification behavior of mafic alkaline magmas. 112 113 2. Methods 114 115 2.1. Experiments 116
The time-series experiments were conducted at the HP-HT Laboratory of Experimental 117
Volcanology and Geophysics of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) in 118
Rome, Italy. A synthetic trachybasaltic starting material was obtained in batches of ~2 gr from pure 119
oxides and carbonates mixed by grinding under ethanol in an agate mortar for ~1 h. This mixture 120
was chosen in order to reproduce one of the most primitive products erupted at Mt. Etna volcano 121
(i.e., the Mt. Maletto formation in Sicily, Italy; Armienti et al., 1988, 2013; Mollo et al., 2015b), as 122
well as mafic alkaline magmas from different and complex intraplate settings in the world (cf. 123
Mollo et al., 2018). A Pt-crucible containing the synthetic powder was loaded in a 1 atm vertical 124
tube CO–CO2 gas-mixing furnace at the NNO+2 buffer. The temperature was kept at 1,100 °C for
125
10 h to ensure decarbonation and then was raised up to 1,600 °C. This temperature was kept 126
constant for 4 h to ensure homogeneous melting. The resulting glass was removed from the Pt-127
crucible and powdered. Backscattered microphotographs and microprobe analyses performed on 128
chips extracted from top, middle, and bottom of the Pt-crucible, demonstrated homogeneity and the 129
absence of crystalline phases in a glass with an average composition (in wt.%) of SiO2 = 50.09
130
(±0.29), TiO2 = 1.49 (±0.1), Al2O3 = 15.92 (±0.18), FeO = 8.09 (±0.13), MgO = 7.60 (±0.16), CaO
131
= 11.97 (±0.20), Na2O = 3.26 (±0.12), K2O = 1.53 (±0.09), and P2O5 = 0.02 (±0.02). In order to
132
minimize iron loss, some aliquots of the powder were previously loaded into the Pt-crucible and run 133
for 3 h at 1,600 °C to pre-saturate the crucible (cf. Conte et al., 2006). The sample holder was then 134
quenched and cleaned in a hot HF solution. The same approach was adopted to pre-saturate the Pt-135
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
capsules (3 mm of outer diameter) used for the piston cylinder experiments conducted at 400 MPa. 136
It is found that the iron loss from the samples was kept to <5% of the initial amount. 137
Piston cylinder experiments were carried out with a non-end loaded apparatus 138
(“QUICKpress”, Depths of the Earth co.) using a 19-mm NaCl-pyrex-graphite-MgO assembly that 139
produced a redox state close to the NNO+2 buffer (Masotta et al., 2012). The assembly was 140
simultaneously loaded with two Pt-capsules containing the nominally anhydrous (dried in oven at 141
110 °C for 48 h) and hydrous (2 wt.% of deionized H2O added with a microsyringe) trachybasaltic
142
glass. The capsules were also surrounded by powdered pyrophyllite to prevent H2O loss and
143
enhance stress homogenization during initial compression (Freda et al. 2001, 2008). After cold 144
pressurization to a nominal pressure 10% higher than desired, the pressure was decreased down to 145
400 MPa, after reaching the final resting temperature. Reversal experiments were carried out by 146
isobarically superheating the starting glass from room temperature up to the superliquidus condition 147
of 1,300 °C (the liquidus temperature of the trachybasalt is 1,200 °C; Del Gaudio et al., 2010; 148
Mollo et al., 2010, 2011) at a rate of 80 °C/min. This temperature was kept constant for 30 min and 149
then decreased down to the target crystallization condition of 1,100 °C using the same rate of 80 150
°C/min. At the superliquidus temperature of 1,300 °C, the relaxation time to reach equilibrium is 151
much shorter than the 30 min for the used trachybasaltic melt (Webb, 1997). For this starting melt 152
composition and the used experimental strategy, relaxation kinetics are extremely rapid in time (i.e., 153
from milli- to micro-seconds) and weakly dependent on the superheating path used in laboratory 154
(Vetere et al., 2013, 2015).The temperature was monitored by a factory-calibrated C-type (W-155
5Re/W-26Re) thermocouple with precision of 3 °C. Considering the limited effect of 2 wt.% H2O
156
on the liquidus region of the trachybasaltic melt, the cooling path produced a nominal undercooling 157
condition relatively fast (ΔT 100-120 °C), as previously experimentally demonstrated for similar 158
starting compositions (Mollo et al., 2013a, 2013b, 2013c). ΔT refers to the difference between the 159
phase-in temperature of the melt and the quench temperature. The isothermal condition was kept 160
constant over variable dwell times of 0.5, 1, 2, 4, 8, and 24 h (Table 1). Then, an isobaric quench of 161 100 °C/s was applied. 162 163 2.2. Analyses 164
Microchemical analyses (Table 1S, 2S and 3S) were performed at the HP-HT Lab of INGV 165
using an electron probe microanalyzer (EPMA) Jeol-JXA8200 with combined EDS-WDS (five 166
spectrometers with twelve crystals). Data were collected using 15 kV accelerating voltage and 10 167
nA beam current. For glasses, a slightly defocused electron beam with a size of 5 μm was used, 168
with a counting time of 5 s on background and 15 s on peak. For crystals, the beam size was 5 μm 169
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
with a counting time of 20 and 10 s on peaks and background respectively. The following standards 170
were used: jadeite (Si and Na), corundum (Al), forsterite (Mg), andradite (Fe), rutile (Ti), orthoclase 171
(K), apatite (P), and spessartine (Mn). Sodium and potassium were analyzed first to minimize alkali 172
migration effects. The precision of the microprobe was measured through the analysis of well-173
characterized synthetic oxide and mineral secondary standards. Based on counting statistics, 174
analytical uncertainties relative to their reported concentrations indicate that precision was better 175
than 5% for all cations. 176
177
2.3. Image processing and textural parameters 178
Microphotographs were collected in backscattered electron (BSE) mode of a field emission 179
gun-scanning electron microscopy (FE-SEM) Jeol 6500F equipped with an energy-dispersive 180
spectrometer (EDS) detector and installed at the HP-HT Lab of INGV. Magnifications from 50× to 181
400× were adopted to collect a statistically representative number of crystals (i.e., clinopyroxene 182
and titanomagnetite) for each different experimental charge. The ImageJ software package was used 183
for image processing. Textural data were determined by thresholding (i.e., segmentation, as showed 184
in Fig.1), counting, and measuring the crystal edges (e.g. Hammer et al., 1999; Brugger and 185
Hammer, 2010a). According to the stereological theorem of Delesse (1847), the area fraction of the 186
minerals investigated equals their volume fraction, provided that the distribution of crystals remains 187
uniform along the entire length of the experimental capsule. Boundaries between touching crystals 188
were identified through the visual inspection of the crystal shapes. The uncertainty introduced by 189
this refining process was considered negligible due to the statistically high number of particles 190
examined for each experimental capsule: 266–1,277 and 376-1,914 crystals for clinopyroxene and 191
titanomagnetite, respectively. The uncertainty related to the quantification of the textural parameters 192
was calculated as 1σ variation of different crystal populations (Tables 2 and 3), thus representing 193
sample heterogeneity rather than the error caused by image processing. A different approach is 194
employed for estimating the uncertainty associated with area fraction (%) measurements. It is 195
apparent that the segmentation process represents the main potential source of error in estimating 196
area fraction, especially for crystals with shapes characterized by high surface-to-volume ratios (e.g. 197
dendritic crystals). Therefore, for each sample, we considered positive and negative errors in area 198
fraction estimates that would arise from addition and subtraction of a pixel layer around each crystal 199
in the binary image. 200
In the case of clinopyroxene, dendritic crystals characterize most of the experimental 201
charges and their multiple intersection with the section plane impeded any reliable crystal size 202
distribution (CSD) analysis (Hammer, 2006; Higgins, 2006; Armienti, 2008). Conversely, other 203
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textural parameters can be effectively quantified in terms of the dimensions of largest crystals (i.e., 204
best-fit ellipse major and minor axis; Fig. 2), the surface area to volume ratio, and the volume 205
fraction. The maximum growth rate (Gmax) of clinopyroxene was measured following one of the 206
most common methods reported in literature (Burkhard, 2002; Hammer and Rutherford, 2002; 207
Couch et al., 2003; Baker, 2008; Iezzi et al., 2011): 208 209 (1) 210 211
Where L and W are the mean length and width, respectively, on the basis of the ten largest crystals 212
for each BSE image, whereas t is the dwell time. The factor 2 refers to the growth of half-crystal 213
during advancement of the pinacoid face. To track the textural evolution of clinopyroxene as a 214
function of dwell time, the surface area to volume ratio ( ) has been also determined according to 215
the method outlined by Hammer (2006, 2009): 216 217 (2) 218 219 and 220 221 (3) 222 223
Where Sv and ϕ are the total interfacial area of the population per unit volume of sample and the 224
fractional volumetric phase abundance. NL is the mean number of boundary intersections per unit 225
length of randomly-oriented test line (cf. Underwood, 1968). The parameter represents the ratio 226
of crystal population surface area to the volume of that population, thus accounting for the 227
difference in volumetric abundances among distinct crystal populations and/or BSE images. This 228
parameter allows to quantify the textural maturation based on the crystal morphology. Moreover, 229
can be hypothetically related to the crystallization conditions of the system (i.e., diffusion- and 230
interface-limited crystallization phenomena), as long as it represents an estimate of the interfacial 231
area developing between the crystal surface and surrounding glass feeding the crystal growth 232
(Lofgren, 1974; Hammer and Rutherford, 2002). 233
In the case of titanomagnetite, the majority of crystals exhibits well-developed, euhedral 234
morphologies enabling reliable CSD analysis. The crystal growth was investigated through the 235
application of three different methods based on the assumption of constant growth kinetics over the 236
adopted dwell time (e.g., Marsh, 1988; Armienti, 2008). In Method 1, Gmax was determined 237
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
following the same approach used for clinopyroxene. In Method 2, the batch growth rate (G) was 238
determined through the expressions (Blundy and Cashman, 2008; Brugger and Hammer, 2010a, 239 2010b): 240 241 (4) 242 243 and 244 245 (5) 246 247 and 248 249 (6) 250 251
Where d, t, , NA, and NV are, respectively, the characteristic crystal size, the experimental time, the 252
area fraction, the area number density (i.e., total number of crystals per unit area), and the 253
volumetric number density. In Method 3, the CSD analysis was performed according to the 254
procedure reported in Armienti (2008), where the stereological correction accounts for the 255
“unfolding” method based on the algorithms of Schwartz (1939) and Saltykov (1949). This allows 256
to consider the cut-section effects (i.e., larger particles contribute to smaller size classes when 257
sectioned by a plane not passing through their center) and intersection-probability effects (i.e., 258
smaller particles are less likely intersected by the section plane; Higgins, 2000, 2006). Despite the 259
shape of CSD curves is strongly dependent on the choice of the bin size, the procedure of Armienti 260
(2008) is optimized by including a routine properly designed for the minimization of the residuals 261
between the measured number of particles and that re-calculated from the CSD (zeroth moment of 262
the distribution) analysis as follow: 263
264
(7)
265 266
and between the measured volume crystal fraction and that resulting from the CSD (third moment 267 of the distribution): 268 269 (8) 270
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 271
Subsequently, the CSD plot is formulated for a given image and the slope of this distribution is 272
determined. The growth rate and the characteristic crystal size were calculated as the ratio between 273
the total length and total number of crystals, expressed as the integral forms of the first and zeroth 274
moments of the distribution, respectively (Randolph and Larson, 1971; Cashman, 1992; Marsh, 275 1998, 2007): 276 277 (9) 278 279 and 280 281 (10) 282 283 284
Where n0 represents the value of the intercept at L = 0 and Ld is the characteristic crystal size. Note 285
that Ld is different from d that, in turn, is the characteristic crystal size determined by the “batch” 286 calculation approach. 287 288 3. Results 289 3.1. Textural data 290 3.1.1. Crystal morphologies 291
Clinopyroxene is the dominant mineral phase in the whole set of experiments (Fig. 3), with 292
area fraction ranging from 35.8% to 53.5% (Table 2 and Fig. 4a). The comparison between 293
anhydrous and hydrous experiments does not show relevant differences in the clinopyroxene 294
content, neither illustrates any significant nor systematic variation with dwell time. Indeed, most of 295
the area fraction measurements overlap within their associated uncertainties (Table 2 and Fig. 4a). 296
Crystal morphologies are prevalently dendritic from 0.5 to 8 h, whereas well-developed textures are 297
observed at 24 h (Figs. 2 and 3). A marked difference in the crystal habit is recognizable between 298
anhydrous and hydrous conditions, with more euhedral and faceted clinopyroxenes found in 299
hydrous experiments (Fig. 3). The mean maximum size of clinopyroxene ranges from 54 µm (0.5 h) 300
to 86 µm (24h) and from 63 µm (0.5 h) to 120 µm (24h) in the anhydrous and hydrous charges, 301
respectively (Fig. 4b). A significant increase in the crystal size occurs only at 24 h and this is 302
particularly evident under hydrous conditions. The parameter does not substantially change at 303
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
0.5, 1, and 2 h, but then starts to decrease as the dwell time increases (Fig. 5). Values of 304
measured under hydrous conditions are, on average, lower than those measured for the anhydrous 305
charges. A marked difference can be observed at 24 h (Fig. 5), where the lower value of hydrous 306
crystallization experiments reflects a higher degree of crystal euhedrality. 307
Titanomagnetite is scarce in the experimental charges, with area fractions variable from 308
0.5% to 2.5% and from 1.4% to 2.4% under anhydrous and hydrous crystallization conditions, 309
respectively (Table 3 and Fig.4c). At 0.5 and 1 h, the amount (0.5-0.8%) of crystals from anhydrous 310
experiments is apparently lower than that (1.4-1.8%) measured in the hydrous ones, despite area 311
fraction estimates are affected by great uncertainties (Fig.4c). Moreover, no clear trends are 312
observed with increasing dwell time (Fig.4c). The titanomagnetite morphology is well-developed 313
with most of the crystals showing euhedral shapes and only rare subhedral (hollow-to-hopper) 314
textures. Highly dendritic morphologies, as those obtained in fast (up to 15 °C/min) cooling rate 315
experiments (Hammer, 2006; Mollo et al., 2013b) are never observed. The mean maximum crystal 316
size varies from 5 µm (0.5 h) to 11 µm (24 h) and from 7 µm (0.5 h) to 23 µm (24 h) under 317
anhydrous and hydrous conditions, respectively (Fig. 4d). These data are comparable with d values 318
calculated through the batch method, and similar trends are also found for Ld from CSD analysis 319
(Table 3). The morphological evolution of titanomagnetite cannot be accurately quantified through 320
the parameter due to the extremely low crystal content and volumetric density of crystals, 321
providing standard deviations close to the measured values. The CSD curves derived for the 322
experimental titanomagnetite grains are showed in Fig. 6 where the natural logarithm of the 323
population density is plotted against the crystal size. As a general rule, larger crystal bins develop 324
with increasing dwell time. The plots exhibit also a gentle downturn at small crystal sizes that, 325
sometimes, is accompanied by a weak upward convexity, more pronounced for crystal populations 326
from 24 h experiments. CSDs from anhydrous time-series are characterized by shallower slopes 327
than those from hydrous experiments. The anhydrous CSD curves display comparable shapes, with 328
lower slopes and intercepts at longer dwell times (Table 3). The hydrous CSD curves are also very 329
similar in terms of crystal populations and shapes, with a subtler decrease in slope and intercept 330
when the dwell time increases from 0.5 to 8 h (Table 3). At 24 h, the crystal population skews 331
significantly towards larger crystal size bins, thus defining a much smoother shape of the CSD (Fig. 332
6 and Table 3). This abrupt deviation is also related to the textural change of clinopyroxene 333
observed at the same dwell time (see discussion below). 334
335
3.1.2. Crystal growth kinetics 336
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
The value of Gmax measured for clinopyroxene ranges from 4.98 × 10-8 to 1.49 × 10-6 cm/s 337
and from 6.94 × 10-8 to 1.80 × 10-6 cm/s under anhydrous and hydrous conditions, respectively 338
(Table 2). The logGmax vs. logt diagram shows that the growth rate decreases with increasing dwell 339
time (Fig. 7). Data from anhydrous and hydrous isothermal time-series overlap within their 340
uncertainties (Table 2 and Fig. 7), with the only exception observed for 24 h charges where the 341
hydrous Gmax is sensibly higher than the anhydrous counterpart. The linear regression fit of the data 342
yields the following equations: 343 344 (11) 345 346 (12) 347 348
The regressed data show an excellent linearity between logGmax and logt (Fig. 7), with a high 349
correlation coefficient (R2 = 0.99). The regression fits are characterized by positive intercepts and 350
negative slopes that, however, do not perfectly overlap due to the different Gmax values measured at 351
24 h. The slope of the log-log linear trend has been proposed to give insights into the rate-limiting 352
process for the crystal growth (i.e., interface- vs. diffusion-limited crystallization regimes; 353
Burkhard, 2005; Orlando et al., 2008), whereas the intercept represents the logarithm of growth rate 354
extrapolated at the time zero. 355
The growth rates of titanomagnetite crystals have been determined through the three 356
methods described above and listed in Table 3. As the dwell time increases, Gmax (Method 1) 357
decreases from 1.48 × 10-7 to 6.62 × 10-9 cm/s and from 2.00 × 10-7 to 1.34 × 10-8 cm/s under 358
anhydrous and hydrous conditions, respectively. The batch growth rate (Method 2) provides values 359
that are one order of magnitude lower than Gmax and ranging from 3.52 × 10-8 to 1.44 × 10-9 360
(anhydrous data) and from 4.64 × 10-8 to 4.04 × 10-9 (hydrous data). Similar estimates have been 361
also derived through the CSD analysis (Method 3). As for the case of clinopyroxene, 362
titanomagnetite crystals with higher growth rates formed over shorter dwell times (Table 3). The 363
logGmax vs. logt diagram exhibits similar linear trends for both anhydrous and hydrous time-series 364
experiments (Fig. 8) that are described by the following equations: 365 366 (13) 367 368 (14) 369 370 (15) 371
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 372 (16) 373 374 (17) 375 (18) 376 377
The regression fits of growth rates calculated through Method 2 and Method 3 show comparable 378
intercepts and slopes, attesting the reliability of estimates. Hydrous experiments show slight slop 379
variations as a function of the different growth rates estimated for the 24 h experiment (Fig. 8). 380
381
3.2. Mineral and melt chemistry 382
Clinopyroxenes from anhydrous (Wo43-46-En37-40-Fs16-19) and hydrous (Wo44-47-En37-41-Fs
15-383
17) experiments are classified as diopside-augite (Table 1S) according to the classification scheme
384
of Morimoto (1988). With respect to the anhydrous charges, the compositions of crystals obtained 385
under hydrous conditions show higher values of Si, Mg-number [Mg# = 100 × Mg/(Mg + Fetot) on
386
molar basis] and diopside + hedenbergite (DiHd), and lower values of tetrahedrally-coordinated 387
aluminum (TAl), Fe3+, enstatite + ferrosilite (EnFs) and Ca-Tschermak + CaTi-Tschermak + CaFe-388
Tschermak (CaTs + CaTiTs + CaFeTs = Ts) (Fig. 9). The mineral chemistry also changes as a 389
function of dwell time. TAl and Fe3+ are preferentially incorporated in clinopyroxenes from 0.5-2 h 390
experiments, whereas Si content increases in crystals from 4 to 24 h charges (Fig. 9). No clear 391
trends are observed for Ti but, from a statistical point of view, its concentration slightly decreases 392
with dwell time, as documented for TAl and Fe3+. Overall, clinopyroxene crystals are progressively 393
enriched in DiHd and depleted in Ts from 4 to 24 h charges (Fig. 9). The compositional change is 394
determined by the kinetically-controlled cation exchange (Si + Mg) (TAl + Fe3+), expanding the 395
Ts stability at the expense of Di over short time durations. Additionally, for each single experiment, 396
strong crystal zoning is recognized either for large euhedral clinopyroxenes or dendritic crystals 397
with analyzable cores and rims. Fig. 10a shows Di-poor and Di-rich clinopyroxene portions in 398
which mineral compositional changes have been evidenced using a high contrast in backscattered 399
electron images highlighting Fe-Mg crystal zoning. Fig. 10b displays also an example of electron 400
microprobe profile analyzed across the crystal and the surrounding glass. A traverse of 5- m-step 401
has been performed for SiO2, MgO, Al2O3, and FeO. By assuming SiO2 and MgO variations as a
402
proxy for Di component in clinopyroxene (Fig. 10b), the crystal zoning is characterized by Di-poor 403
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
(Di43-44) and Di-rich (Di46-48) compositions. It is apparent that complex zoning patterns develop by
404
the overgrowth of Di-rich and well-faced crystals onto early-formed Di-poor dendrites (Fig. 10a-b). 405
Titanomagnetite exhibits an almost constant composition in all the experimental charges 406
(Table 2S), showing Al2O3 (8.9-10.1 wt.%) and MgO (5.4-5.8 wt.%) enrichments typically
407
observed under rapid crystal growth conditions (Mollo et al., 2013b). On the other hand, the amount 408
of TiO2 (3.8-4.2 wt.%) is relatively low, translating to an ulvospinel (Usp) content almost close to 1
409
mol.% (Table 2S). Overall, the Ti–Al–Mg cationic substitutions in titanomagnetite indicate kinetic 410
effects where Al + Mg are more easily incorporated into disequilibrium crystals by lowering the 411
number of Ti cations (Mollo et al., 2013b). 412
The residual glass composition (Table 3S) shifts from trachyandesite to basaltic 413
trachyandesite (54.1-56.1 wt.% SiO2, 6.4-8.1 wt.% Na2O+K2O and Mg#50-54) and from trachybasalt
414
to tephrite (45.6-48.9 wt.% SiO2, 6.2-7.8 wt.% Na2O+K2O and Mg#50-54) under anhydrous and
415
hydrous crystallization conditions, respectively (data on anhydrous basis according to Le Bas et al., 416
1986). No clear glass compositional trends are found as a function of dwell time in both anhydrous 417
and hydrous charges. The interstitial glass develops within a complex crystal framework causing 418
marked compositional heterogeneity. This applies frequently in short dwell time experiments, 419
where small glass pockets are isolated by dense dendrite crystallization where the variable contents 420
and compositions of crystals induce, locally, strong glass chemical changes. On the other hand, 421
microprobe chemical profiles performed in more abundant glass portions surrounding large and 422
isolated crystals do not show concentration gradients next to the clinopyroxene surface (i.e., up to 423
30 m far from the crystal-glass interface; Fig. 10a-b). 424
425
4. Discussion 426
427
4.1. Textural maturation of clinopyroxene 428
Under both anhydrous and hydrous conditions, the experimental charges obtained at 0.5, 2, 429
4, and 8 h are characterized by small clinopyroxenes with dendritic habits, whereas large and 430
euhedral crystals develop at 24 h. Due to the strong kinetic effects at the onset of crystallization, the 431
maximum size (65 µm on average) of clinopyroxene does not substantially change as the dwell time 432
increases from 0.5 to 8 h, whereas longer crystal lengths (100 µm on average) are measured at 24 h 433
(Table 2). Within the time interval of 0.5-8 h, the size, content and growth rate of clinopyroxene do 434
not differ significantly nor systematically between hydrous and anhydrous time-series experiments, 435
suggesting the lack of complete equilibrium. Following the theory of nucleation proposed by the 436
pioneer study of Kirkpatrick (1983), the activation energy required for the onset of nucleation is 437
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
proportional to the number of tetrahedral units expressed as either Al–O bonds or the most energetic 438
Si–O bonds in the crystallizing silicate melt. A great number of tetrahedral units and corner 439
connections implies a high nucleation barrier, which in turn determines high incubation times 440
(Kirkpatrick, 1983). The clinopyroxene crystal structure comprises a few tetrahedral units, so that a 441
relatively low number of structural re-arrangement is expected in the melt, translating to a short 442
nucleation delay and the attainment of high area fractions (Fig. 4a). The occurrence of dendrites is 443
addressed to melt supersaturation (e.g. Lofgren, 1974; Sunagawa, 1981) due to imposition of a 444
thermodynamic driving force promoting early crystal nucleation rather than growth (e.g. Hammer, 445
2006, 2008). Figs. 2 and 3 highlight that, upon the effect of a large degree of initial undercooling, 446
clinopyroxene dendrites from 0.5-8 h experiments are composed of tiny crystallites aligning along 447
branches that are perpendicular to each other (i.e., different orders of branch generations; Faure et 448
al., 2003). When the experimental charge is maintained isothermally for 24 h, dendrite branches 449
change into the prismatic and well-faced morphologies. The annealing treatment of 24 h before 450
quench causes melt relaxation (i.e., equilibration) phenomena that are more effective with respect to 451
the shorter dwell times (Dingwell & Webb, 1990; McMillan and Wolf, 1995; Moynihan, 1995; 452
Webb and Dingwell, 1995). Coherently, the growth of dendrites is less favored in more relaxed melt 453
regions characterized by lower degrees of melt supersaturation (i.e., “Berg effect”; Berg, 1938). The 454
lack of dendritic shapes in 24 h experiments (Fig. 3) points to a textural maturation of 455
clinopyroxene documented typically under equilibrium conditions when crystallization takes place 456
from a fully relaxed melt (Baker, 2008; Mollo et al., 2011, 2013c) or, alternatively, under extremely 457
low degrees of undercooling when the growth rate largely exceeds the nucleation rate (Simakin et 458
al., 2003; Orlando et al., 2008). Rationally, after the early effect of undercooling, the diffusion-459
limited growth of dendrites occurring at shorter dwell times (i.e., more effective melt saturation), 460
translates to a steady-state regime under which euhedral crystals more favorably develop by 461
interface-limited growth at longer dwell times (i.e., more effective melt relaxation; Figs. 2 and 3). 462
Well-faced morphologies in natural magmatic products, as those attained in porphyritic 463
intrusions, are classically addressed to a high-temperature coarsening process of the small crystal 464
populations over time (e.g., Park and Hanson, 1999; Higgins, 1998, 1999, 2011). In crystallization 465
experiments conducted on analogue materials, Means and Park (1994) observed the evolution from 466
dendritic to blocky crystal habits as related to segmentation of the dendrite branches and further 467
coarsening of the resulting tiny crystals. A similar effect could be potentially applied to the 468
decreasing area fraction of clinopyroxene observed for anhydrous experiments (Fig. 4a). However, 469
due to the presence of scattered data affected by large uncertainties (up to ±12.4% on average; see 470
Table 2), no clear trends can be delineated for both anhydrous and hydrous time-series experiments 471
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
(Fig. 4a). Alternatively, crystal growth mechanisms by dendrite attachment have been documented 472
by both ex-situ (Pupier et al., 2008) and in-situ (Schiavi et al., 2009) laboratory observations 473
conducted on basaltic melts. More specifically, these experiments reveal that the growth histories of 474
individual crystals may proceed by intervals of relatively uniform free growth, abrupt size increase 475
by grain coalescence, and growth reduction by impingement (Schiavi et al., 2009). Coalescence 476
takes place when adjacent tiny crystals of similar orientation attach to form one 477
(crystallographically) single crystal (Pupier et al., 2008). Additionally, coalescence phenomena can 478
take place between crystals that are initially misaligned, thus involving further grain rotation 479
(Schiavi et al., 2009). As the crystal fraction increases substantially, crystal impingement and 480
overgrowth become the most important textural maturation mechanisms (Schiavi et al., 2009). 481
Further experimental studies have demonstrated that attachment of tiny dendritic crystals can 482
effectively lead to the formation of large homogeneous clinopyroxenes and plagioclases (Iezzi et 483
al., 2011, 2014; Vetere et al., 2013, 2015). This is in agreement with the theory of aggregation by 484
self-orientation of sub-micrometric crystals along crystallographic directions, in order to attain 485
minimization of interfacial energies (Kostov and Kostov, 1999; Alivisatos, 2000; Banfield et al., 486
2000; Deer et al., 2001; Niederberger and Colfen, 2006; Sear, 2012; Teng, 2013). A similar 487
attachment feature has been observed for the formation of large plagioclase crystals due to volatile 488
exsolution and degassing of a fluid-saturated magma rising from depth (Crabtree and Lange, 2011; 489
Frey and Lange, 2011). During flowage onto the surface, naturally cooling Hawaiian and Etnean 490
lava flows may be characterized by massive crystallization (up to ~60 vol.%) of microphenocrysts 491
and microlites. In this context, the crystal growth is driven by attachments of clinopyroxene and 492
plagioclase phenocrysts with lengths up to 1 mm, having also important implications for the 493
rheological behavior of lava flows (Crisp and Baloga, 1990; Crisp et al., 1994; Cashman et al., 494
1999; Soule et al., 2004; Lanzafame et al., 2013; Mollo et al., 2015). In naturally undercooled 495
olivines, zoning patterns reveal a crystallization history marked by early diffusion-limited growth of 496
interconnected branches forming a skeletal framework (Welsh et al., 2014; Shea et al., 2015). When 497
undercooling decreases after the fast growth stage, the skeletal branches are partially infilled to 498
yield well-faceted polyhedral crystals, as growth becomes interface-limited (Shea et al., 2015). 499
Turning to the textural maturation of clinopyroxenes from this study (Figs. 2 and 3), it cannot be 500
excluded that infilling of the early dendrite frameworks attaching to form a larger crystal takes 501
place with the annealing time. Dendritic clinopyroxene crystals may represent an early diffusion-502
limited morphology caused by the large degree of initial undercooling and partly preserved by short 503
annealing treatments. The melt is readily supersaturated in the slow-diffusing Al cationsfavoring 504
the early growth of Di-poor dendrites (Fig. 10a-b) by the kinetically-controlled exchange (Si + Mg) 505
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
(TAl + Fe3+) (Mollo et al., 2010; 2012a; 2013a). Subsequently, Di-rich overgrowths develop 506
from the residual melt that becomes substantially enriched in SiO2 and MgO components (Fig.
507
10b). Melt relaxation and crystal attachment start to be effective phenomena when the temperature 508
is maintained isothermally and, at this condition, the interface-controlled regime becomes more 509
effective. As a consequence, early-formed Di-poor skeletal branches are partially infilled by the 510
SiO2-MgO-rich melt, leading to the formation of Di-rich overgrowths (Fig. 10a-b). The transition
511
between diffusion-limited to interface-limited morphologies through attachment and infilling of 512
early dendrite branches may also explain the lack of a clear trend between clinopyroxene area 513
fraction and dwell time (Fig. 4a), especially in hydrous experiments where the cation diffusivity in 514
the melt is enhanced (Zhang et al., 2010). 515
The parameter of clinopyroxene progressively decreases with increasing dwell time 516
(Table 2 and Fig. 5), evidencing that more euhedral morphologies are attained at 24 h by the 517
textural maturation of the dendritic crystal habits. This corroborates the observation of Hammer 518
(2006, 2009) that can be effectively used to quantify the degree of crystal euhedrality. From an 519
energetic point of view, is directly proportional to the free energy change during melt 520
solidification and represents part of the crystallization free energy term related to the development 521
of crystal-melt interfaces (Hammer, 2006). Hence, the decreasing trend showed in Fig. 5 is an 522
expression of the minimization of the free energy as the grain boundaries approach to equilibrium 523
with the surrounding melt. This is consistent with what observed in the logG vs. logt diagrams 524
derived for clinopyroxene (Fig. 7) and titanomagnetite (Fig. 8). The slopes of the log-log linear 525
trends exhibit almost comparable values of ~0.7-0.9 that are invariably higher than the theoretical 526
threshold of 0.5 derived under diffusion-limited crystal growth conditions (Müller-Krumbhaar, 527
1975; Burkhard, 2002, 2005; Orlando et al., 2008). On this basis, it can be inferred that the decrease 528
of crystal growth with dwell time is mostly related to the progressive approach to (near-)equilibrium 529
crystallization where attachment/detachment reactions of cations from the melt onto the crystalline 530
surface (and vice versa) occur at the same rate. A similar interpretation has been given by Orlando 531
et al. (2008), documenting that growth kinetics of plagioclase from trachybasaltic melts are 532
generally faster than clinopyroxene, as the former exhibits steeper log-log linear trends with slopes 533
close to 1. According to Orlando et al. (2008), at 1170 °C, plagioclase equilibrates with the melt in 534
a shorter time interval of 3 h, whereas clinopyroxene requires a longer time of 20 h that, 535
importantly, is similar to the longest dwell time used in this study. 536
The values of Gmax reported in Table 2 are highly comparable with those measured by 537
previous authors for clinopyroxenes growing from similar basaltic and trachybasaltic melts. For 538
hydrous hawaiitic melts, Simakin et al. (2003) measured Gmax from 1.85 10-5 to 2 10-6 cm/s 539
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
when cooling rate experiments were quenched after 0.5 h. Such data are in agreement with the high 540
growth rates determined at the shortest dwell time adopted for the time-series experiments. 541
Conversely, the low growth rates attained at 24 h match with those derived in the fast cooling rate 542
experiments of Burkhard (2002) conducted on Hawaiian basalts. The in-situ observations performed 543
by Ni et al. (2014) confirm that, after 1.5 h, the growth rate of clinopyroxene is comprised 544
between 1.7 10-6 and 6 10-7 cm/s, resembling values from 0.5-8 h time-series experiments. 545
Remarkably, data from Baker (2008) are very close to results from this study, as the author adopted 546
a comparable undercooling condition (ΔT = 75 °C) and a similar trachybasaltic melt from Mt. Etna 547
volcano. For clinopyroxenes with dendritic, skeletal and swallowtail textures, Baker (2008) 548
estimated growth rates comprised between 5.4 × 10-7 and 9.4 × 10-8 cm/s for dwell times between 549
3.5 and 14 h. In comparison with natural studies, CSD analyses performed by Oze and Winter 550
(2005) on natural basalts yield clinopyroxene growth rates variable from 3.74 × 10-6 to 1.00 × 10-8 551
cm/s over crystal residence times of ~0.04-9 h (Table 2). In contrast, the static experiments of 552
Burkhard (2005) on re-heated anhydrous basaltic glasses (dwell times of 22-576 h at 930-990 °C 553
and 1 atm), and the low undercooling (ΔT = 20 °C) experiments of Orlando et al (2008) on seeded 554
anhydrous trachybasalts (dwell times of 3-40 h at 1170 °C and 1 atm), resulted in growth rates up to 555
one order of magnitude lower than those from this study (Fig. 11). According to a great number of 556
authors (e.g. Dowty, 1980; Lofgren & Russell, 1986; Lesher et al., 1999; Conte et al., 2006; Mollo 557
et al., 2013b), rapid crystallization kinetics are usually attained in experiments employing high 558
degrees of undercooling or cooling rate. The lower slopes of log-log trends from Orlando et al. 559
(2008) stands for the smaller degrees of undercooling used to approach equilibrium crystal sizes 560
with respect to dendrites developed during time-series experiments (Fig. 11). This reflects distinct 561
crystallization mechanisms operating at different degrees of undercooling (e.g. Kirkpatrick, 1975; 562
Sunagawa, 2005; Faure et al., 2007; Ni et al., 2014). Indeed, at low degrees of undercooling, the 563
textural maturation proceeds through screw dislocation and layer-by-layer growth determining 564
smooth growth surfaces and euhedral morphologies, while at higher degrees of undercooling crystal 565
nucleation dominates resulting in dendritic and skeletal morphologies. Log-log trends from the 566
experiments of Burkhard (2005) show an overall slope of ~1 (Fig. 11), confirming the achievement 567
of equilibrium crystal sizes for clinopyroxenes annealed over 20-24 h. 568
569
4.2. Textural maturation of titanomagnetite 570
Titanomagnetite crystals have strong tendency to attain euhedral habits at the shortest dwell 571
time of 0.5 h (Table 3). The extremely fast textural maturation documented in this study can be 572
addressed to the high interfacial energies occurring between oxide crystals and silicate melts 573
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
(Hammer, 2006). This effect is enhanced by the application of an isothermal temperature after rapid 574
cooling rate conditions, as demonstrated by Mollo et al. (2012a) who compared two sets of identical 575
cooling rate experiments, the first immediately quenched after cooling and the second kept at the 576
final temperature over a certain time. It is also important to note that small titanomagnetites 577
nucleate, sometimes, on the tip of branches formed by clinopyroxene dendrites (Fig. 3). According 578
to cooling rate experiments conducted on basaltic melts by Hammer et al. (2010), there is a 579
preferential epitaxial relationship between the {110}timt and {010}cpx faces, resulting from
580
heterogeneous nucleation of tiny titanomagnetite crystals on dendrite branches of clinopyroxene. 581
Moreover, compositional gradients arising during dendrite growth may provide a further 582
thermodynamic driving force for heterogeneous nucleation of chemically different phases 583
(Kirkpatrick, 1975; Walker et al., 1976; Hammer, 2006; Mollo et al., 2012b). This textural 584
relationship becomes less frequent with increasing dwell time, especially when the textural 585
maturation produces larger and euhedral clinopyroxene crystals (Fig. 3). Energetically unfavorable 586
grain boundaries develop as the growth rate prevails over the nucleation rate, causing an increase in 587
the surface energy associated with the crystal-crystal interface relative to the crystal-melt one 588
(Hammer et al., 2010). The maximum size (10 µm on average) of titanomagnetite slightly changes 589
from 0.5 to 8 h, but then increases significantly (23 µm on average) in hydrous experiments 590
equilibrated for 24 h (Table 3). The titanomagnetite growth rates (Gmax > Gbatch ≈ GCSD) invariably 591
decrease with increasing dwell time (Table 3 and Fig. 8). This relationship is confirmed by the 592
intercept values of log-log trends, representing growth rates extrapolated at the time zero. The value 593
of Gmax is up to five times higher than those of GCSD and Gbatch, resembling data (from 1.2 10-8 to
594
3.5 10-9 cm/s) obtained from the heating experiments of Burkhardt (2002, 2005). With respect to 595
natural titanomagnetites studied by Oze and Winter (2005), the growth rates from CSD analysis of 596
time-series experiments largely overlap those estimated from phenocryst populations modelled at 597
residence times of 0.12-6 h. 598
Log-log linear trends for titanomagnetite show slopes shallower than those derived for 599
clinopyroxene (see Eq.12a-c and Eq.13a-c; Figs. 7 and 8), indicating prolonged growth of the 600
former crystal phase (Orlando et al., 2008). This is also evidenced by the counterclockwise rotation 601
of the CSD curves as a function of time (Fig. 6). Although the CSD analysis of experimental 602
products cannot be directly matched to that of natural rocks, the evolution of scale invariant 603
parameters (such as the slope) allows to evaluate the interplay between nucleation and growth 604
mechanisms. The fan-like evolution of CSDs is typically observed in natural and experimental 605
igneous systems (e.g. Waters & Boudreau, 1996; Marsh, 1998; Pupier et al., 2008; Schiavi et al., 606
2009), in which an increased importance of growth vs. nucleation reflects the progressive evolution 607
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
of the melt composition and the decreasing liquidus temperature with increasing crystal content 608
(e.g. Cashman, 1993; Hammer, 2008). Generally, for equivalent dwell times, titanomagnetite CSD 609
curves from hydrous experiments exhibit slopes slightly shallower than crystal populations from 610
anhydrous charges. Under hydrous crystallization conditions and high degrees of undercooling, 611
Muncill and Lasaga (1988) observed an increased crystal growth rate with respect to early 612
anhydrous experiments (Muncill & Lasaga, 1987), responding to crystallization kinetics enhanced 613
by the effect of water on cation diffusivity in the melt (e.g., Dowty, 1980; Davis et al., 1997; 614
Lasaga, 1998; Hammer, 2008; Calzolaio et al., 2010; Zhang, 2010). Nevertheless, at dwell times of 615
24 h, a striking difference is observed in the titanomagnetite crystalline population, exhibiting 616
skewness towards larger sizes and drastically shallower slopes (Fig. 6 and Table 3). In this respect, 617
the attainment of euhedral textures for clinopyroxene crystals at the same dwell times may have 618
influenced the textural development of titanomagnetite crystals, causing shift from heterogeneous 619
nucleation to a growth-dominated crystallization regime. Intriguingly, a downturn of the CSD curve 620
is observed in almost all the experiments at the smaller crystal size bins (Fig. 6). This effect has 621
been previously interpreted as an inadequate spatial resolution of the analyzed images (Hammer et 622
al., 1999; Higgins, 2006; Armienti, 2008), the evidence of textural coarsening (e.g., Higgins, 1998, 623
1999, 2011; Ni et al., 2014), or a decrease of the nucleation rate with decreasing the residual melt 624
volume (Marsh, 1998). However, BSE microphotographs show a high resolution that, in most 625
cases, is less than one micron. Moreover, the observed fan-like evolution of CSD curves cannot be 626
accounted by the sole decrease of nucleation rate with time that, in turn, is mostly restricted to area 627
fractions higher than 50% in a closed system (Marsh, 1998). Indeed, the ex-situ cooling 628
experiments of Pupier et al., (2008) and the in-situ textural observations conducted by Schiavi et al. 629
(2009) attest that fanning evolution and the concave downward curve at the small grain size results 630
from a decrease in the number of small grains in favor of large grains over time (i.e., Ostwald 631
ripening and grain coalescence). 632
633
4.3. Crystal growth vs. cation diffusivity in the melt 634
One intriguing feature from time-series experiments presented in this study is the lack of 635
clear concentration gradients in the glass surrounding the clinopyroxene crystals (Fig. 10a-b) that is 636
apparently in contrast with the complex textures and compositions, as well as the overall increase in 637
DiHd relative to Ts with increasing dwell time (Fig. 9). It is known that a high degree of 638
undercooling favors a diffusion-limited crystallization regime accompanied by the development of a 639
diffusive boundary layer in the melt next to the growing crystal face (Dowty, 1980; Lofgren and 640
Smith, 1980; Kirkpatrick, 1981; Hammer, 2008; Mollo and Hammer, 2017). The deviation from 641
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
homogeneous equilibrium increases, as the crystal growth rate greatly exceeds the diffusion rates of 642
chemical species in the melt (Kirkpatrick, 1981). Compositional gradients develop in the melt 643
feeding the crystal growth, so that cations compatible with the crystal lattice are depleted in the melt 644
near the crystal surface, whereas the incompatible cations are rejected from the advancing crystal 645
surface and enriched in the adjacent melt (Kirkpatrick, 1981). Mollo et al. (2013a, 2013c) 646
conducted cooling rate experiments on the same trachybasaltic melt used in this study, with the 647
difference that the charges were immediately quenched at the end of cooling and no dwell times or 648
annealing times were applied before quenching. The authors observed that the composition of 649
clinopyroxene is sympathetic with the enrichment or depletion of cations in the diffusive boundary 650
layer supplying nutrients to the advancing crystal surface, responding to the cation exchange (Si + 651
Mg) (TAl + Fe3+). It is worth stressing that the thickness of the diffusive boundary layer at the 652
crystal-melt interface decreases with dwell time, as the chemical species are more efficiently 653
rejected away from the crystal surface (Dowty, 1980; Lofgren and Smith, 1980). The melt becomes 654
fully relaxed and all chemical gradients cease when the diffusing chemical components have 655
sufficient time to re-equilibrate with the original bulk composition of the far-field melt (Kirkpatrick, 656
1981; Baker, 2008). Disequilibrium cation partitioning during rapid crystal growth may also takes 657
place in presence of a very thin diffusive boundary layer around the growing crystals (Watson and 658
Muller, 2009). This is especially true for low viscosity melts, such as trachybasalts at Mt. Etna 659
volcano, so that the thin diffusive boundary layer is limited to the region affected by cation 660
interactions with the crystal surface (Watson and Muller, 2009). According to the experiments of 661
Baker (2008), after initial undercooling, the clinopyroxene growth rate significantly decreases with 662
time, causing the concentration gradients in the melt adjacent to the crystal surface to decrease by 663
diffusive relaxation. The same applies to melt inclusions where their entrapment require interface-664
limited phenomena where an early rapid crystal growth forms melt embayments. Subsequently, a 665
period of slow growth is necessary to seal and isolate the embayment during interface-limited 666
textural maturation (e.g., Stewart and Pearce 2004; Blundy and Cashman 2005). Data from this 667
study confirm that Gmax decreases by one order of magnitude with dwell time from 0.5 to 24 hours, 668
favoring the shift from a diffusion-limited to an interface-limited crystallization regime (Fig. 7). 669
Therefore, the lack of an analyzable diffusive boundary layer next to the crystal surface may be 670
addressed to 1) the decreasing crystal growth rate with dwell time 2) the fast diffusivity of cations 671
in the trachybasaltic melt and 3) the development of a thin diffusive boundary layer close to the 672
spatial resolution limits of the microprobe. The diffusion coefficients (D) of cations compatible (Mg 673
and Ca) and incompatible (Al and Na) with clinopyroxene crystal lattice have been calculated 674
through the equations 23 (DMg = 5-6 × 10-13 m2/s), 24 (DCa = 6-7 × 10-12 m2/s) and 36 (DAl = 8-9 × 675
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
10-14 m2/s) reported in the review study of Zhang et al. (2010), as well as through equation SEBD 676
(DNa = 7-8 × 10-10 m2/s) reported in Chen and Zhang (2009). Note that these equations were derived 677
by the regression fit of anhydrous experimental data, consequently, the calculated diffusion 678
coefficients represent a conservative limit for the cation mobility in the melt that, in turn, is 679
enhanced by the effect of H2O. The isothermal temperature of 1,100 °C was used as input data for
680
calculations, together with the average analyses of glasses from experimental charges, representing 681
the quenched melt feeding the clinopyroxene growth. Assuming absence of convection fluxes in the 682
experimental capsules, the cation diffusion length d was derived as follows (Baker, 2008): 683
684
(19)
685 686
In the log-log diagram presented in Fig. 12a, the diffusion length (logd) is plotted against the 687
experimental dwell time (logt). During clinopyroxene growth by dendrite attachment, the size of 688
single and isolated dendrites varies from 5 to 50 m under both anhydrous and hydrous 689
conditions. This range is comparable with the logd calculated for Al and Mg at 0.5 and 1 h (Fig. 690
12a). In contrast, at 24 h, the dendrite size is always lower than d, suggesting that the diffusivity in 691
the melt is fast enough to supply fresh cations from the far-field (relaxed) melt to the advancing 692
crystal surface (Fig. 12a). Moreover, from 0.5 to 24 h dwell times, all the dendrites with size lower 693
than 12 m do never intercept the travelling distance of Al (i.e., the slow-diffusing incompatible 694
cation). Evidently, when the experimental charges were cooled from the superliquidus condition 695
down to the isothermal temperature of 1,100 °C, the melt was rapidly supersaturated in Al by the 696
fast nucleation and growth of Di-poor dendrites. However, the diffusive boundary layer developing 697
at the dendrite-melt interface was extremely thin, so that the system readily shifted from diffusion-698
limited to interface-limited conditions, favoring the overgrowth of Di-rich crystals. To test this 699
hypothesis, the 1-dimensional “disequilibrium” crystal growth equation derived by Watson and 700
Muller (2009) has been used to model how the early enrichment of Al in clinopyroxene dendrites is 701
controlled by the thickness of the diffusive boundary layer in the melt. Importantly, Al is rate-702
limiting for the disequilibrium growth of clinopyroxene due to its slow diffusivity in the melt phase 703
(cf. Iezzi et al., 2011, 2014; Mollo et al., 2013a, 2013c). Moreover, Al is incompatible with 704
clinopyroxene crystal lattice and its concentration increases in the diffusive boundary layer as the 705
crystal growth rate increases. Data from this study show that the partition coefficient (KAl) of Al 706
measured at the clinopyroxene-glass interface decreases from 0.77 to 0.45 with increasing dwell 707
time. According to the kinetically-controlled cation exchange (Si + Mg) (TAl + Fe3+), the 708
concentration of TAl in clinopyroxene decreases from 0.43 apfu for the disequilibrium (Di-poor) 709
